Topological Classification of points in $Z^2$ by using Topological Numbers for $2$D discrete binary images

In this paper, we propose a topological classification of points for 2D discrete binary images. This classification is based on the values of the calculus of topological numbers. Six classes of points are proposed: isolated point, interior point, simple point, curve point, point of intersection of 3 curves, point of intersection of 4 curves. The number of configurations of each class is also given.